Question

1. \\(\overline{cd}\\) is the midsegment of trapezoid wxyz.

a. what is the value of \\(x\\)?
b. what is xy?
c. what is wz?

Explanation:

Step1: Recall midsegment formula for trapezoid

The midsegment of a trapezoid is the average of the two bases. So, \( CD=\frac{WZ + XY}{2} \). Here, \( WZ=x + 3 \), \( CD = 22 \), and \( XY=4x + 1 \). Substitute into the formula: \( 22=\frac{(x + 3)+(4x + 1)}{2} \).

Step2: Solve for \( x \)

Multiply both sides by 2: \( 44=(x + 3)+(4x + 1) \). Combine like terms: \( 44 = 5x+4 \). Subtract 4: \( 40 = 5x \). Divide by 5: \( x = 8 \).

Step3: Find \( XY \)

Substitute \( x = 8 \) into \( XY = 4x+1 \): \( XY=4(8)+1=32 + 1=33 \).

Step4: Find \( WZ \)

Substitute \( x = 8 \) into \( WZ=x + 3 \): \( WZ=8 + 3=11 \).

Answer:

a. \( x = 8 \)
b. \( XY = 33 \)
c. \( WZ = 11 \)